On Thursday, the retailer revealed that the credit card information of 40 million customers who shopped at its U.S. stores between Nov. 27 and Dec. 15 was compromised, resulting in customers' names, card numbers, expiration dates, and short verifications codes (known as a card’s “CVV”) potentially falling into the hands of identity thieves. (At the moment, it appears that online purchases made during this time have not been affected by the breach.)

While Target investigates the matter and how it happened, it advised its customers to keep an eye on bank accounts and immediately report any suspected fraud to their bank. What else can you do if you’re worried you may be one of the 40 million affected? We spoke to experts to find out.

Run your credit report. Under federal law, you are entitled to one free copy of your credit report every 12 months, says Neil Chase, vice president of education at LifeLock. Visit AnnualCreditReport.com or call 877-322-8228 to run a credit check. If you notice anything suspicious, you’ll want to request that the credit reporting agency delete that information from your file. While verifying that a purchase is fraudulent can be a lengthy process, Andrew Schrage of the financial advice website MoneyCrashers says, “In most cases, and particularly for credit cards with purchase protection included, they will work with you and investigate the transaction.”

Monitor your transactions. Keep an eye on the activity on your credit and debit cards, looking out for any charges that don't seem to be yours, says Chase. Instead of waiting for your monthly statement to arrive, check in on your account online, or use a transaction-monitoring tool, like the one offered by LifeLock, he adds.

Report suspicious transactions immediately. As soon as you see something that doesn't look right, contact your card issuer. (You can find the phone number on the back of your card, Chase says).

Get new cards -- even if you haven't seen any suspicious charges. This will help prevent any future fraud, Schrage says. “This is particularly important if you believe your debit card PIN number was compromised and you use the same PIN on your other accounts as well.”